Assume G is an At-group. G satisfies a weak chain condition if its every Ai-subgroup is contained in an Ai+1-subgroup for all i ⩾ 1. We study two proper subclasses of the class of the At-groups satisfying a weak chain condition, and the extreme case of the At-groups satisfying a chain condition.
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Zhang et al. (2024) studied this question.
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